1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Salsk061 [2.6K]
3 years ago
12

Question 1 (13 marks) A charge Q is located on the top-left corner of a square. Charges of 2Q, 3Q and 4Q are located on the othe

r corners as shown above in the Figure. Assuming each side of the square is 5cm in length, and the charge Q= 2.5 µC, determine the net force exerted on the 2Q charge due to the other charges.

Physics
1 answer:
tino4ka555 [31]3 years ago
3 0

Answer:

F = 45 (2.4142 i ^ + 4.414 j ^)

  F = 226.40 N,           θ= 61.3

Explanation:

For this exercise we will use that the forces are vectors and we will add them, the force due to being electric charges must comply, go Coulomb's law

         F₁₂ = k q₁ q₂ / r₁₂²

To apply this equation to our case, they indicate that all charges are of the same sign and their value, also the charge Q is located in the upper left corner, unfortunately the diagram of the other charges is not loaded, but the most general is that is in sequence, see attached, for the sum of the forces let's add its components

x-axis (horizontal)

         Fₓ = F₂₁ + F₂₄ₓ

Let's use trigonometry for the force component, as the weathering figure is a square the angle between the force and the x axis is 45

        cos 45 = F₂₄ₓ / F₂₄

         F₂₄ₓ = F₂₄ cos 45

y-axis (vertical)

        F_{y} = F₂₃ + F_{24y}

        sin 45 = F_{24y} / F₂₄

        F_{24y} = F₂₄ sin 45

let's search every distance

The side of the square is worth l = 5cm = 0.05 m

we can find the diagonal with the Pythagorean theorem

         d = √(l² + l²) = l √2

now we can search every force

         F₂₁ = k q₁ q₂ / r₁₂²

         F₂₁ = k Q 2Q / l²

         F₂₁ = k 2Q² / l²

this force points in the positive x direction

         F₂₃ = k q₂ q₃ / r₂₃²

         F₂₃ = k 2Q 3Q / l²

this force points in the direction of the positive y

         F₂₄ = k q₄q₂ / d²

         F₂₄ = k 4Q 2Q / 2 l²

let's find the resultant in each x

X axis

        Fₓ = k 2Q² / l² + k 8Q² / 2 l²    cos 45

        Fₓ = k 2Q² / l² (1 + 4/2 cos 45)

        Fₓ = k 2Q²/ l²   2.4142 i ^

Axis y

       F_{y} = k 6Q² / l² + k 8Q² / 2 l²    sin 45

       F_{y} = k 2Q² / l² (3 + 4/2 sin45)

       F_{y} = k 2Q² / l² (4,414)

       

the resultant force

       F = Fₓ i ^ + F_{y} j ^

       F = k 2Q² / l²      ( 2.4142 i ^ + 4.414 j ^)

       

let's substitute the values

       F = 9 10⁹ 2 (2.5 10⁻⁶) 2 / 0.05²      (2.4142 i ^ + 4.414 j ^)

       F = 45 (2.4142 i ^ + 4.414 j ^)

The result we can give is this form and in the form of module and angle

             

let's use the Pythagorean theorem to find the modulus

            F =√ (Fₓ² +  F_{y}²)

            F = 45 √ (2.4142² + 4.414²)

            F = 226.40 N

we use trigonometry for the angle, measured from the x-axis

           tan θθ = Fy / Fx

          θ  = tan⁻¹ (4.414 / 2.4142)

           θ= 61.3

You might be interested in
Hello please help i’ll give brainliest
malfutka [58]

Acceleration is the rate of change in an object's velocity

3 0
3 years ago
Radio waves travel 300,000,000 m/s. The frequency is 101,700,000. ehats the wavelength​
Nesterboy [21]

Answer:

we have formula of frequency :

frequency(f)= speed of sound(c)/wavelength(λ)

for wavelength we swipe it with frequency as follows

λ=c/f

λ=300,000,000/101,700,000

λ=2.949

8 0
3 years ago
A circular loop of wire has radius of 9.50 cmcm. A sinusoidal electromagnetic plane wave traveling in air passes through the loo
m_a_m_a [10]

Answer:

The induced emf  is  \epsilon  = 0.1041 \  V  

Explanation:

From the question we are told that

   The  radius of the circular loop is  r =  9.50 \ cm  =  0.095 \ m

     The  intensity of the wave is  I  =  0.0215 \ W/m^2

      The wavelength is  \lambda =  6.90\ m

Generally the intensity is mathematically represented as

         I  =  \frac{ c *  B^2  }{ 2 * \mu_o  }

Here  \mu_o is the permeability of free space with value  

         \mu_o  =  4 \pi *10^{-7} N/A^2

B is the magnetic field which can be mathematically represented from the equation as

          B  =  \sqrt{ \frac{ 2 *  \mu_o  *  I  }{ c} }

substituting values

          B  =  \sqrt{ \frac{ 2 *  4\pi *10^{-7} *   0.0215  }{ 3.0*10^{8}} }

          B  =  1.342 *10^{-8} \  T

The  area is mathematically represented as

       A =  \pi r^2

substituting values

       A =  3.142 *   (0.095)^2

       A = 0.0284

The angular velocity is mathematically represented as

        w =  2 *  \pi  *  \frac{c}{\lambda }

substituting values          

       w =  2 *  3.142   *  \frac{3.0*10^{8}}{ 6.90 }  

        w =  2.732 *10^{8} rad  \ s^{-1}  

Generally the induced emf is mathematically represented as

        \epsilon  =  N *  B  *  A  *  w * sin (wt )

At maximum induced emf  sin (wt)  =  1

    So

         \epsilon  =  N *  B  *  A  *  w

substituting values

         \epsilon  = 1  *    1.342 *10^{-8}   *  0.0284  *2.732 *10^{8}  

         \epsilon  = 0.1041 \  V  

         

7 0
3 years ago
What tool is used to measure air pressure?
alukav5142 [94]
A<span> barometer is used to measure air pressure. </span>
8 0
3 years ago
The phenomenon of vehicle "tripping" is investigated here. The sport-utility vehicle is sliding sideways with speed v1 and no an
Mrrafil [7]

Answer:

v_1  = 3.5 \ m/s

Explanation:

Given that :

mass of the SUV is  = 2140 kg

moment of inertia about G , i.e I_G = 875 kg.m²

We know from the conservation of angular momentum that:

H_1= H_2

mv_1 *0.765 = [I+m(0.765^2+0.895^2)] \omega_2

2140v_1*0.765 = [875+2140(0.765^2+0.895^2)] \omega_2

1637.1 v_1 = 3841.575 \omega_2

\omega_2 = \frac{1637.1 v_1}{3841.575}

\omega _2 = 0.4626 \ v_1

From the conservation of energy as well;we have :

T_2 +V_{2  \to 3} = T_3 \\ \\ \\  \frac{1}{2} I_A \omega_2^2 - mgh =0

[\frac{1}{2} [875+2140(0.765^2+0.895^2)](0.4262 \ v_1)^2 -2140(9.81)[\sqrt{0.76^2+0.895^2} -0.765]] =0

706.93 \ v_1^2 - 8657.49 =0

706.93 \ v_1^2  = 8657.49

v_1^2  =  \frac{8657.49}{706.93 }

v_1 ^2 =  12.25

v_1  = \sqrt{ 12.25

v_1  = 3.5 \ m/s

6 0
3 years ago
Other questions:
  • PLZZZZ HELP!!!
    11·1 answer
  • An 11-year-old girl’s height increased by several inches in three months. Which example of the characteristics of life is most s
    6·2 answers
  • Which statement is true about an airplane wing during flight
    13·1 answer
  • What type of energy to high frequency waves have?
    14·1 answer
  • Car A hits car B (initially at rest and of equal mass) frombehind while going 35 m/s. Immediately after the collision, car Bmove
    7·1 answer
  • Which scientific term is defined as the rate at which work is accomplished?
    5·1 answer
  • How can you safely experiment with plants during a scientific investigation?
    10·2 answers
  • Which group of stars is represented by the line image
    10·2 answers
  • What are the three ways to lessen any risk?
    7·2 answers
  • An 8.38 gram sample of water lost 870 J of heat. What is the change in temperature
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!